Ultrasonics 56 (2015) 505–511

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Ultrasonics

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Simultaneously measuring thickness, density, velocity and attenuationof thin layers using V(z, t) data from time-resolved acoustic microscopy

http://dx.doi.org/10.1016/j.ultras.2014.09.0190041-624X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: mbfju@zju.edu.cn (B.-F. Ju).

Jian Chen a,b, Xiaolong Bai a, Keji Yang a, Bing-Feng Ju a,⇑a The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, People’s Republic of Chinab Centre for Optical and Electromagnetic Research, Zhejiang Provincial Key Laboratory for Sensing Technologies, State Key Laboratory of Modern Optical Instrumentation,Zhejiang University, Hangzhou 310058, China

a r t i c l e i n f o

Article history:Received 30 October 2013Received in revised form 27 September 2014Accepted 29 September 2014Available online 20 October 2014

Keywords:Thin layerMechanical and geometrical propertiesTime-resolved acoustic microscopyV(z, t) dataReflection spectrum

a b s t r a c t

To meet the need of efficient, comprehensive and automatic characterization of the properties of thin lay-ers, a nondestructive method using ultrasonic testing to simultaneously measure thickness, density,sound velocity and attenuation through V(z, t) data, recorded by time-resolved acoustic microscopy isproposed. The theoretical reflection spectrum of the thin layer at normal incidence is established as afunction of three dimensionless parameters. The measured reflection spectrum R(h, x) is obtained fromV(z, t) data and the measured thickness is derived from the signals when the lens is focused on the frontand back surface of the thin layer, which are picked up from the V(z, t) data. The density, sound velocityand attenuation are then determined by the measured thickness and inverse algorithm utilizing leastsquares method to fit the theoretical and measured reflection spectrum at normal incidence. It has thecapability of simultaneously measuring thickness, density, sound velocity and attenuation of thin layerin a single V(z, t) acquisition. An example is given for a thin plate immersed in water and the resultsare satisfactory. The method greatly simplifies the measurement apparatus and procedures, whichimproves the efficiency and automation for simultaneous measurement of basic mechanical and geomet-rical properties of thin layers.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Evaluating material properties of thin layers by an ultrasonicnon-destructive method has various applications in judging theadhesive quality of thin layers, characterizing the protective coat-ings on the surfaces of automobiles, determining the uniformityof ultra-thin foils and so on. In order to realize the non-destructiveevaluation of thin layers by applying ultrasound, it is required toinspect the mechanical integrity using a criterion that indicatesthe change in acoustic and geometrical properties of the material[1]. For this purpose, the thin layer parameters including the thick-ness, density, sound velocity and attenuation that are sensitive todefects and material properties should be measured accurately,and their interactions need to be well established.

However, the techniques for determining the acoustic propertiesof thin layers are extremely limited compared with those for bulkmaterials. Associated with the transducer type, the acoustic tech-niques for characterizing thin layers are divided into two catego-ries: one is performed with a flat transducer, another with a

focused transducer. The flat transducer method has been success-fully used to characterize thin layers. Kim et al. use a broadbandPVDF flat transducer to measure the longitudinal wave speedtraveling along the thickness direction in a thin material [3].Kannajosyula et al. extract the phase information of successive ech-oes for the simultaneous estimation of thicknesses and ultrasonicvelocities of individual layers in a two layered media, but thismethod requires the total thickness of the sample to be known[4]. Tohmyoh et al. developed an acoustic resonant spectroscopytechnique for measuring the acoustic impedance, ultrasonic veloc-ity, and density of micron-scale polymer films using a non-focusedultrasonic transducer. It can be used to characterize the thin filmprepared without a substrate, but it requires the interface betweenthe films to be examined and the plate vacuum sealed, and thus theexperimental set-up is complex [5]. Besides, the lateral resolutionof the flat transducer is poor, and it cannot be used to accuratelymeasure the local geometrical and acoustical properties of a thinlayer. But there is no such limitation with a focused transducer. Fur-thermore, the focused ultrasound has the advantage of greatlyreducing the effects of the parallelism of the interfaces and thequality of the specimen surface on the measured results, comparedto the unfocused beam. The feasibility of characterizing a thin layer

Fig. 1. The schematic of a three-layered structure.

506 J. Chen et al. / Ultrasonics 56 (2015) 505–511

with highly focused ultrasound has also been demonstrated. Hänelhas succeeded in simultaneously measuring the sound velocity andthe thickness of poly film using time-resolved acoustic microscopy,but it requires manually focusing the lens on the front and back ofthe sample, and the automation of the measurement cannot beachieved [6]. Raum et al. used a highly focused 50 MHz broadbandtransducer to generate longitudinal and lateral waves in thin corti-cal bone sections, then determined the confocal locations andtimes-of-flight of individual echoes through pulse separation usinga Hanning window. From these values the sample thickness, as wellas longitudinal and lateral sound velocities, were determined usinga specially developed iterative analysis algorithm [7]. Zinin et al.characterized the elastic moduli and density of a thin, transverselyisotropic layer on a substrate based solely on surface acoustic wavemeasurements in an acoustic microscope. This method requires thethin layer to be prepared with a substrate, and the Rayleigh wavespeed in the layer higher than the shear wave speed in the sub-strate. Furthermore, the mode structure of surface acoustic wavesis fairly complicated, and hard to process [8]. In all of the aforemen-tioned techniques, the main attention was given to measuring somespecific properties of thin layers and none of them can be used tomeasure thickness, density, sound velocity and attenuation of a thinlayer simultaneously. Moreover, manual intervention is required,which brings difficulties to the automatic application.

In order to meet the need of efficient, comprehensive and auto-matic characterization for the properties of thin layers, a kind ofsimultaneous measurement method for the thickness, density,sound velocity and attenuation using V(z, t) data is proposed, andthe V(z, t) data is the pulse-echo trays of the reflections from thefront and back surface of the specimen as a function of the trans-ducer-specimen distance recorded by time-resolved acousticmicroscopy. In the second section, the normal theoretical reflectionspectrum as a function of three dimensionless parameters and theinverse algorithm utilizing the least squares method are described.The measuring principle for the thickness and acoustic reflectionspectrum using V(z, t) data are presented in Section 3. An experi-mental example for simultaneous measurement of thickness, den-sity, sound velocity and attenuation of a thin stainless steel plateby using a point-focusing transducer with nominal frequency ofaround 50 MHz is described in Section 4 and measurement resultsfor the experiment are given to validate the proposed method, ver-ifying that it is feasible for practical application.

2. Theoretical model

2.1. The theoretical reflection spectrum of a thin layer at normalincidence

As shown in Fig. 1, a three-layered model consisting of twoknown substrates separated by a thin layer is studied. Time-harmonic normal incident longitudinal waves are considered. Thetheoretical reflection spectrum of a thin layer at normal incidenceis given by [10]

RthðxÞ ¼R12 þ R23e2ixs2

1þ R12R23e2ixs2ð1Þ

where x is the angular frequency and s2 = h/c2 is time-of-flight inthe thin layer. R12 = (Z2�Z1)/(Z2 + Z1) and R23 = (Z3�Z2)/(Z3 + Z2) arethe reflection coefficients at the front and back interface of the thinlayer, and Zi = qici (i = 1, 2, 3) is the acoustic impedance with qi andci being its density and sound velocity respectively. The phase shiftsxs2 can also be expressed as k2h with k2 = x/c2 being the wavenumber, h is the thin layer thickness. For a viscoelastic thin layer,k2 is complex impedance, i.e. k2 ¼ k02 þ ik002, and k002 is thefrequency-dependent attenuation term. When the substrate 1 is

the same as substrate 3, the above theoretical reflection spectrumcan be simplified as follows

RthðxÞ ¼R12ð1� e2 ixs2Þ

1� R212e2 ixs2

ð2Þ

From Eqs. (1) and (2), it can be seen that Rth(x) depends on fourindependent thin layer properties including thickness h, density q,sound velocity c2 and attenuation a. In order to reduce the numberof the independent parameters, Eq. (2) can be rewritten as follows,so that the theoretical reflection spectrum at normal incidencedepends only on three dimensionless parameters [2]

RthðxÞ ¼ð1� ZNÞð1� e2ix�hð1þi�aÞÞ=ð1þ ZNÞ

1� ðð1� ZNÞ=ð1þ ZNÞÞ2 e2ix�hð1þi�aÞð3Þ

where ZN = Z2/Z1 is the impedance ratio, �a ¼ k002=k02 is the dimension-less attenuation and �h = hx0/c2 is the dimensionless thickness, inwhich x0 = 1 MHz is the normalization constant. Thus, the theoret-ical reflection spectrum of the thin layer at normal incidence is afunction of frequency x and three dimensionless parameters i.e.ZN, �h; �a.

2.2. Inverse algorithm to determine the dimensionless parameters

The reflection spectrum at normal incidence is fully defined bythe three dimensionless parameters of ZN, �h and �a. To determinethese dimensionless parameters, an inverse algorithm utilizingthe least square method to minimize the sum of squared devia-tions between the theoretical and measured reflection spectrumat normal incidence is adopted

minx�R3

12

XN

n¼1

ðjRmeðx;xnÞj � Rthðx;xnÞjÞ2 ð4Þ

where N is the number of data points at the different frequenciesover the ultrasonic transducer bandwidth. x is a set that consistsof the three dimensionless parameters, Rth is the theoretical reflec-tion spectrum at normal incidence and Rme is the normal compo-nent of the measured reflection spectrum R(h, x) which will bedescribed in the next section.

J. Chen et al. / Ultrasonics 56 (2015) 505–511 507

3. Measurement methodology

3.1. The thickness measurement of a thin layer

Since the reflection spectrum at normal incidence depends onthe three dimensionless parameters, the four independent thinlayer properties of thickness, density, sound velocity and attenua-tion cannot be decoupled sufficiently. However, thickness can beknown by a prior measurement.

The thickness measurement mechanism by focused acousticmicroscopy is schematically shown in Fig. 2, in which (a) is thespherical lens focusing on the front surface and (b) on the back sur-face, respectively. The echo S1 is reflected from the front surfacewhen the lens is focusing on the front surface of the thin layer.The echo S2 and S3 come from the front and back surface of the thinlayer respectively, while the lens is focusing on the back surface ofthe thin layer. Together with geometric relationships, these echoescan be used to determine the thickness of the thin layer [6]

h ¼ 12�1

2A2 tan2 bþ A

14

A2 tan4 bþ c20

cos2 b

� �1=2( )1=2

� ðD t2Þ ð5Þ

where A = c0Dt1/Dt2, Dt1 and Dt2 are the time-of-flight differencesbetween echoes S1, S2 and between echoes S2, S3, respectively. b isthe half aperture angle and c0 is the sound velocity of the couplingfluid.

3.2. The normal reflection spectrum measurement of a thin layer

The thin layer thickness is measured with a focused transducer,according to the signals when the lens is focusing on the front andback surface of the thin layer. Meanwhile, the normal reflectionspectrum should be measured in order to determine to the restparameters. Considering the spatial and temporal structure of theacoustic field, and according to our former work, the reflectionspectrum R(kz, x) and V(z, t) of a thin layer have the relationshipof:

Rðkz;xÞ ¼Fz;tðVðz; tÞe�2ik0zÞFz;tðV0ðz; tÞe�2ik0zÞR0ðkz;xÞ ð6Þ

where kz = k0 cos h is the z component of the wave number andk0 = x/c0 = 2pf/c0, f is the frequency, c0 is the sound velocity of thecoupling fluid. Fz,t(�) represents the two-dimensional Fourier trans-formation operation. V(z, t) is the pulse-echo trays when thefocused transducer move along z-axis vertically, the vertical axis z

Fig. 2. The thickness measurement mechanism by point-focusing acousticmicroscopy.

means the distance away from the focal plane and the horizontalaxis t means the time-of-flight. V(z, t) and V0(z, t) are the acquiredresponse from specimen and reference material respectively. Simi-larly, R(kz, w) and R0(kz, w) are the two dimensional reflection spec-trum of specimen and reference material respectively. Moreover, asa reference material, its reflection coefficient should be constantwithin the incident aperture angle. The detailed measurement ofthe two-dimensional reflection spectrum with focused transducercan be found in our former work (Ref. [9]).

The frequency band is assigned according to two consider-ations; (1) Will be due to the band limit of the transducer, as theresults for both very low and high frequency ranges in the bandare not evident. (2) According to the sensitivity of the reflectioncoefficient to the thin layer properties, the local minima in thereflection spectra should be incorporated in the frequency rangefor the inversion, because of the high value of the sensitivity func-tion in this range [2]. As the frequency/angle band is assigned, thenoise gain caused by V0 is not very evident.

According to Eq. (6) and the relationship of h = cos�1(kz/k0), thereflection spectrum R(h, x) can be calculated from R(kz, x), and thereflection spectrum at normal incidence can be determined fromthe reflection spectrum R(h, x) at h = 0.

For the purpose of performing the V(z, t) data acquisition, thesample interval Dz must meet the requirement of

Dz < p=k0 ð7Þ

As the thickness is known, and dimensionless parameters of ZN, �hand �a are determined by the inversion of the measured normalreflection spectrum utilizing the least squares method, the otherthree parameters can be given as

C2 ¼ hx0=�h ð8Þ

q ¼ ZNZ1=c2 ð9Þa ¼ �ax=c2 ð10Þ

where x is the attenuation measuring frequency.

4. Experiments

4.1. Experimental setup

The experimental setup for the time-resolved acoustic micros-copy is schematically shown in Fig. 3. A point focusing transduceris applied with a nominal central frequency of 50 MHz and a�6 dB bandwidth of 60%. A pulser/receiver (Model 5900, OlympusNDT Corporation, Japan) working in the short-pulse mode isapplied. The output signal of the transducer is amplified and thendigitized at a sampling rate of 200 MHz by an 8-bit A/D card(NDT-AD-82G-PCI, Acquisition Logic Company, USA). The verticaltranslation of the transducer, which is used to measure the two-dimensional reflection spectrum of the specimen, is performed bythe z axis of a linear motor driving stage with a repeatable accuracyof 0.5 lm. According to the upper limitation of the transducer band-width and Eq. (7), the spatial sampling interval Dz should be lessthan 10 lm, combined with the consideration of focusing accuracy.Dz is chosen to be 1 lm.

The transducer has a focal length of 12.8 mm in water and thewidth of the active aperture is 6.35 mm, and the half apertureangle is calculated as h ¼ sin�1ð6:35=2

12:8 Þ ¼ 14:4�. Thus, the half aper-

ture angle should be calibrated first. A standard 1 mm stainlesssteel calibrator is used to calibrate the effective half aperture angle.At first, the lens was focused on the front surface, and the A-scantrace was recorded. Then the transducer was moved down verti-cally, and according to the amplitude of the second echo, thenfocus the lens on the rear side of the calibration block, and recordthe A-scan trace again. From these two signals, the time interval

θ

Fig. 3. The experimental setup for time-resolved acoustic microscopy.

Fig. 4. The magnitude of two-dimensional spectrum of (a) Reference material and (b) thin stainless steel plate. (k = k0(1 � cos h) is spatial frequency.)

508 J. Chen et al. / Ultrasonics 56 (2015) 505–511

Dt1 is measured to be 7048 ns and Dt2 354 ns. Substitutingh = 1000 lm, c0 = 1481 m/s, Dt1 and Dt2 into Eq. (5), the half aper-ture angle is calculated to be 10.5�.

A stainless steel block with a roughness of 0.63 lm andthickness of 30 mm was chosen as the reference material for the

purpose of obtaining the geometrical response of the transducer.Its reflection coefficient varies from 0.9363 to 0.9349, which is flatenough and can be deemed as a constant within the incident aper-ture angle. The magnitude spectrum of 2D Fourier transform ofV0(z, t) is shown in Fig. 4(a).

Fig. 5. (a) Two-dimensional reflection coefficients of the thin plate; (b) corresponding normal reflection spectrum.

Fig. 6. V(z) curves for front and back echoes at peak frequency.

J. Chen et al. / Ultrasonics 56 (2015) 505–511 509

4.2. Results and discussion

A thin stainless steel plate with a thickness of approximately200 lm was selected to verify the feasibility of the proposedmethod. The frequency band in a range from 30 MHz to 60 MHzwas assigned to perform the inverse algorithm. Due to the bandlimit of the transducer, the results for both very low and high fre-quency ranges in the band are not evident. Therefore, choosing aproper frequency range is essential.

The amplitude spectrum of 2D Fourier transform of V(z, t)acquired from the thin stainless steel plate is shown in Fig. 4(b).The gray scale represents the normalized amplitude of the two-dimensional spectrum. The vertical axis x is the angular frequencyand the horizontal axis k is the spatial frequency defined ask = k0(1 � cos h). From the definition of spatial frequency, itdepends on the angular frequency k ¼ xð1� cos hÞ=c. Thus, atdifferent frequency points, the maximum of k is different. So theblank part (white triangle zone on the right side) has nosignificance.

From the amplitude spectrum of the plate and the referencematerial, the two-dimensional reflection spectrum of the specimenas a function of spatial frequency k and angular frequency x can bederived according to Eq. (6), as shown in Fig. 5(a), which is a gray-scale image of the two dimensional reflection spectrum R(h, x). Fora layered structure, as the leaky lamb waves are dispersive, thereflection coefficients are frequency dependent. It can be foundthat at different frequencies the minima corresponding to the lambmodes are different, and the lamb mode near the sound axis is notevident because of the poor angular resolution at small incidenceangles.

As the aperture angle of the used focusing transducer is small,only one lamb mode exists. And there is a relationship between leakyLamb modes and reflection coefficient zeroes for a fluid-coupledelastic layer. Therefore, in the case where the density of the couplingfluid is less than that of the plate, the same as in this research, thelamb waves have no significant effects on the reflection coefficients.

The measured reflection spectrum at normal incidence corre-sponding to k = 0 is plotted in Fig. 5(b).

By using Hanning windows (1.5 � pulse duration), the V(z)curves for the echoes of front and back surfaces at peak frequencyof 45 MHz are shown in Fig. 6. Fig. 7(a) shows the echo and itszoom view picked up from V(z, t) data when the lens focusing on

the front surface of the layer, corresponding to peak position ofthe front echo V(z) curve. Due to the AD card limitation, the max-imum and minimum allowable output value are +1 V and �1 V,respectively. Thus, In Fig. 7(a), the negative amplitude is saturated.Here we decide the value using the intermediate value of satura-tion zone. When the lens is focusing on the back surface of thelayer, the echo and its zoom view is illustrated in Fig. 7(b). Accord-ing to Fig. 7(a) and (b), the time-of-flight difference Dt1 is mea-sured to be 1654 ns and Dt2 is 82.8 ns. With respect to Eq. (5)and the velocity of water c0 is 1481 m/s at 20�, the thickness is cal-culated to be 234.7 lm.

The initialization of �h needs to be chosen close to its true value,since it is crucial for its small convergence zone as the inverse algo-rithm is performed. From the definition of �h, it can be determinedby the measured time-of-flight difference Dt2. The initialization forZN, �h and �a, and the results determined by the inversion of themeasured normal reflection spectrum are listed in Table 1. Thetheoretical curve calculated with the determined results is alsoplotted in Fig. 5(b). Since the thickness of the thin plate is obtained,the density, sound velocity and attenuation can be calculated fromZN, �h and �a by Eqs. (8)–(10).

Fig. 7. Measured pulse echoes. (a) Front echo when the lens is focusing on the front of the layer; (b) front and back echoes with the lens focusing on the back surface of thelayer.

Table 1Initialization values and measured results of dimensionless parameters.

�h ZN �a

Initialization 0.0415 50 0.08Results 0.0414 30.28 0.0352

Fig. 8. The thickness of the stainless steel plate measured by using opticalmicroscopy technique.

Table 2Experimental results and truth value of the properties for the thin stainless steel.

h (lm) V (m/s) q (kg/m3) a (Np/m at 50 MHz)

Measured values 234.7 5669 7911 7.576Reference values 230.7 5650 7900 7.528Relative error 1.73% 0.34% 0.14% 0.048%

510 J. Chen et al. / Ultrasonics 56 (2015) 505–511

After ultrasonic measurement, for comparison, the thickness,density and sound velocity are specially measured by well-established techniques. Thickness was measured with a side-viewmicroscope (VHX-600, Keyence, Japan), as shown in Fig. 8. Densityis measured by Archimedes’ method, sound velocity is obtainedthrough time-of-flight technique and attenuation is measured bythrough transmission method. The results measured by ultrasonicmethod are comparable with the true values, as summarized inTable 2.

The determined material properties are comparable. The thick-ness, density and sound velocity can have percentage biases lessthan 5% and the sound attenuation is close to the true value. Theproposed method for simultaneous characterization of thickness,density, sound velocity and attenuation of the thin layer is vali-dated, and it is feasible for practical application.

5. Summary

This paper presented a new method for simultaneously charac-terizing the full set of geometrical and acoustical properties of athin layer by using V(z, t) data recorded by time-resolved acoustic

J. Chen et al. / Ultrasonics 56 (2015) 505–511 511

microscopy. A point-focusing transducer with nominal frequencyof 50 MHz was applied for simultaneously characterizing the thick-ness, density, sound velocity and attenuation of a thin stainlesssteel plate. The results demonstrate that the thickness, densityand sound velocity can be measured with percentage biases lessthan 5% and where the sound attenuation is close to true value.Moreover, the proposed method allows simultaneous characteriza-tion in a single V(z, t) acquisition, thus greatly simplifying the mea-surement apparatus and procedures, improving the efficiency andautomation in simultaneously measuring the basic mechanical andgeometrical properties of the thin layer, and it is especially suitablein characterizing the coatings that cannot be intentionally dam-aged and the substrate that is unable to be exposed as referencematerial.

Acknowledgements

This work is supported by the National Natural Science Founda-tion of China project (No. 51175465), Science Fund for CreativeResearch Groups of National Natural Science Foundation of China(No. 51221004), the National Basic Research Program of China(973 Program, No. 2011CB706505) and the Zhejiang ProvincialNatural Science Foundation of China under Grants (Nos.Z1110393 and LZ13E050001), the Specialized Research Fund forthe Doctoral Program of Higher Education (20120101110059). Itwas also supported by the Fundamental Research Funds for the

Central Universities (No. 2014FZA5002) and China PostdoctoralScience Foundation under Grant No. 2014M551729.

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